Question

The force between two short bar magnets with magnetic moments \( M_1 \) and \( M_2 \) whose centers are \( r \) meters apart is 8 N when their axes are in the same line. If the separation is increased to \( 2r \), the force between them is reduced to:

• A. \( 4N \)
• B. \( 2N \)
• C. \( 1N \)
• D. \( 0.5N \)

Hint:

For magnetic dipole interactions:
- The force follows \( F \propto \frac{1}{r^4} \) for aligned dipoles.
- If the separation doubles, force reduces by a factor of \( 16 \).

Answer 1

The Correct Option is D

Step 1: The force between two bar magnets varies inversely as the fourth power of the distance:
\[ F \propto \frac{1}{r^4} \]
Step 2: If the separation increases to \( 2r \), the new force is:
\[ F' = \frac{8}{2^4} = \frac{8}{16} = 0.5N \]